{"id":34941,"date":"2023-10-21T13:13:24","date_gmt":"2023-10-21T07:43:24","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=34941"},"modified":"2023-11-10T11:51:29","modified_gmt":"2023-11-10T06:21:29","slug":"factorization-when-binomial-is-common","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/factorization-when-binomial-is-common\/","title":{"rendered":"Factorization when Binomial is Common | What is a Common Binomial?"},"content":{"rendered":"

Students can find the factors for an algebraic expression when one of its factors is binomial. Find given algebraic expression Factorization<\/strong><\/a> when Binomial is Common Factor. All related problems are included in this article along with a clear explanation. Therefore, students can practice every problem available in this article and improve their knowledge. The process of solving the factorization problem is very simple if you follow the procedure we explained below. Go through the complete article and learn different methods to solve factorization problems.<\/p>\n

Factorization of Algebraic Expressions when Binomial is Common<\/h2>\n

Follow the simple and easy guidelines on Factorization of Algebraic Expressions When Binomial is Common. They are as follows<\/p>\n

Step 1: In the first step, find the common binomial factor.
\nStep 2: Note down the given expression as the product of this binomial and the quotient obtained on dividing the given expression by this binomial.<\/p>\n

Solved Examples on Factorization When Binomial is a Common<\/h3>\n

1.\u00a0Factorize the algebraic expressions.<\/p>\n

(i) 7b(3x – 4y) + 3a(3x – 4y)<\/p>\n

Solution:
\nGiven expression is 7b(3x – 4y) + 3a(3x – 4y)
\nIn the given expression, the binomial factor is (3x – 4y) as it is common in both terms.
\nTake the (3x – 4y) common and multiply it with the remained terms.
\n(3x – 4y) (7b + 3a)<\/p>\n

The final answer is (3x – 4y) (7b + 3a)<\/p>\n

(ii) 12(9a + 6b)\u00b2 – 4(9a + 6b)<\/p>\n

Solution:
\nGiven expression is 12(9a + 6b)\u00b2 – 4(9a + 6b)
\n12 (9a + 6b) (9a + 6b) -4(9a + 6b)
\nIn the given expression, the binomial factor is (9a + 6b) as it is common in both terms.
\nTake the (9a + 6b) common and multiply it with the remained terms.
\n(9a + 6b)(12(9a + 6b) – 4)
\n(9a + 6b)(108a + 72b – 48)
\nThe final answer is (9a + 6b)(108a + 72b – 48)<\/p>\n

2. Factorize the expression 10r(m \u2013 2n) – 8m + 16n<\/p>\n

Solution:
\nGiven expression is 10r(m \u2013 2n) – 8m + 16n
\nLets take -8m\u00a0 + 16n from the above equation.
\nTake -8 common from -8m + 16n
\n-8(m – 2n)
\nPlace -8(m – 2n) in 10r(2m \u2013 4n) – 8m + 16n equation.
\n10r(m \u2013 2n) -8(m – 2n)
\nIn the above expression, the binomial factor is (m – 2n) as it is common in both terms.
\nTake the (m – 2n) common and multiply it with the remained terms.
\n(m – 2n)(10r – 8)<\/p>\n

The final answer is (m – 2n)(10r – 8)<\/p>\n

3. Factorize (a \u2013 4b)^2 \u2013 7a + 28b<\/p>\n

Solution:
\n(a – 4b)(a – 4b) \u2013 7a + 28b
\nGiven expression is (a – 4b)(a – 4b) \u2013 7a + 28b
\nLets take \u2013 7a + 28b from the above equation.
\nTake -7 common from \u2013 7a + 28b
\n-7(a – 4b)
\nPlace -7(a – 4b) in (a – 4b)(a – 4b) \u2013 7a + 28b equation.
\n(a – 4b)(a – 4b) – 7(a – 4b)
\nIn the above expression, the binomial factor is (a – 4b) as it is common in both terms.
\nTake the (a – 4b) common and multiply it with the remained terms.
\n(a – 4b)(a – 4b – 7)<\/p>\n

The final answer is (a – 4b)(a – 4b – 7)<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can find the factors for an algebraic expression when one of its factors is binomial. Find given algebraic expression Factorization when Binomial is Common Factor. All related problems are included in this article along with a clear explanation. Therefore, students can practice every problem available in this article and improve their knowledge. The process … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34941"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=34941"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34941\/revisions"}],"predecessor-version":[{"id":92678,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34941\/revisions\/92678"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=34941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=34941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=34941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}